42k^2+2k-20=0

Solution for 42k^2+2k-20=0 equation:

Simplifying
42k2 + 2k + -20 = 0

Reorder the terms:
-20 + 2k + 42k2 = 0

Solving
-20 + 2k + 42k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + k + 21k2) = 0

Factor a trinomial.
2((-5 + -7k)(2 + -3k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -7k)' equal to zero and attempt to solve:

Simplifying
-5 + -7k = 0

Solving
-5 + -7k = 0

Move all terms containing k to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -7k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7k = 0 + 5
-7k = 0 + 5

Combine like terms: 0 + 5 = 5
-7k = 5

Divide each side by '-7'.
k = -0.7142857143

Simplifying
k = -0.7142857143
Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve:

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3k = 0 + -2
-3k = 0 + -2

Combine like terms: 0 + -2 = -2
-3k = -2

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {-0.7142857143, 0.6666666667}